Role of noise in a market model with stochastic volatility
Dipartimento di Fisica e Tecnologie Relative, Group of Interdisciplinary Physics, Università di Palermo, Viale delle Scienze, 90128 Palermo, Italy
Revised: 18 September 2006
Published online: 20 October 2006
We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES effect in our model with stochastic volatility. We investigate the role of the correlation between the two noise sources on the NES effect.
PACS: 89.65.Gh – Economics; econophysics, financial markets, business and management / 02.50.-r – Probability theory, stochastic processes, and statistics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.75.-k – Complex systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006